A phase varying apparatus for automobile engine utilizing helical splines has been disclosed in Patent Document 1 cited below. (See for example FIGS. 1 and 2 of Patent Document 1.) The apparatus of Patent Document 1 consists of: an outer hollow cylindrical portion 10 subjected to a torque transmitted from the crankshaft; an inner hollow cylindrical portion 20 integrally connected with the camshaft; and an intermediate member 30 in engagement with helical splines (17, 32, 32, 33) provided between the outer hollow cylindrical portion 10 and inner hollow cylindrical portion 20, the intermediate member 30 having a square male screw portion 31 that engages with the female screw 45 formed inside a brake drum 41. The intermediate member 30 is moved by the square male and female screws (31 and 15) in the axial direction or the camshaft (to the right in FIG. 1) when a brake drum 44 is acted upon by a braking force exerted by an electromagnetic braking means 40, which causes the helical splines (17, 23, 32, and 33) to rotate the inner hollow cylindrical portion 20 (camshaft 2) relative to the outer hollow cylindrical portion 10 (sprocket 12). As a consequence, the phase angle of the camshaft is changed relative to the crankshaft, thereby changing the valve timing.    PATENT DOCUMENT 1 JPA Early Publication H2002-364314